Analyze this conic section to answer the questions below. \( x^{2}=16(y-6) \) A. (Type an ordered pair.) B. The answer is undefined. What are the values of a and b for this conic section? Select the correct choice below and fill in any answer boxes in your choice. B. and b does not have a value not have a value and \( \mathrm{b}- \) C. The answer is undefined. Determine the vertex or vertices for the conic section. A. This conic section has a vertex at \( (0,6) \). B. This conic section has a vertex at \( (2,1) \). C. This conic section has vertices at \( (21,0) \) and \( (2,0) \). D. This conic section has vertices at \( (4,0) \) and \( (-4,0) \).

The given equation \( x^{2} = 16(y - 6) \) represents a parabola that opens upwards. The vertex of this parabola can be found directly from the equation. Here, the vertex is determined from the standard form equation \( x^{2} = 4p(y - k) \), where \((h, k)\) is the vertex. In this case, it is clear that the vertex is at the point \( (0, 6) \). For the parameters \( a \) and \( b \), this parabola can be expressed as \( y = \frac{x^{2}}{16} + 6 \) indicating that \( a = \frac{1}{16} \) and \( b \) is not defined in this context as it usually refers to parameters in other types of conic sections like ellipses or hyperbolas. Thus, the vertex of the conic section is indeed at \( (0, 6) \).